• Zhangyun Tan LISTIC EA 3703, University Savoie Mont Blanc
  • Maxime Moreaud IFP Energies nouvelles, rond-point de l’echangeur de Solaize, BP 3, 69360 Solaize
  • Olivier Alata Laboratoire Hubert Curien, CNRS UMR 5516, Jean Monnet University of Saint-Etienne
  • Abdourrahmane M. Atto LISTIC, EA 3703, University Savoie Mont Blanc



auto-regressive field, fractional Brownian field, HRTEM imaging, mathematical morphology, texture analysis


This paper addresses the characterization of spatial arrangements of fringes in catalysts imaged by High Resolution Transmission Electron Microscopy (HRTEM). It presents a statistical model-based approach for analyzing these fringes. The proposed approach involves Fractional Brownian Field (FBF) and 2-D AutoRegressive (AR) modeling, as well as morphological analysis. The originality of the approach consists in identifying the image background as an FBF, subtracting this background, modeling the residual by 2-D AR so as to capture fringe information and, finally, discriminating catalysts from fringe characterizations obtained by morphological analysis. The overall analysis is called ARFBF (Auto-Regressive Fractional Brownian Field) based morphology characterization. 

Author Biography

Maxime Moreaud, IFP Energies nouvelles, rond-point de l’echangeur de Solaize, BP 3, 69360 Solaize

Project leader

Image processing and analysis.

Control, Signal and System Department

Mechatronics, Computer Science and Applied Mathematics Division



Akaike, H.

(1974). A new look at the statistical

model identification. IEEE Transactions on

Automatic Control, 19(6):716 – 23.

Alata, O. and C. Cariou

(2008a). Two-Dimensional Signal Analysis,

Chapter "2-D Linear Stochastic Modeling",

chapter 2, Pp. 65–114. ISTE, Wiley.

Alata, O. and C. Cariou

(2008b). Two-Dimensional Signal Analysis,

Chapter "2-D Spectral Analysis", chapter 3,

Pp. 115–74. ISTE, Wiley.

Alata, O., C. Cariou, C. Ramananjarasoa, and

M. Najim

(1998). Classification of rotated and scaled

textures using HMHV spectrum estimation

and the Fourier-Mellin transform. In

IEEE Int. Conf. Image Processing, ICIP,

volume 1, Pp. 53–6.

Alata, O. and C. Olivier

(2003). Choice of a 2-D causal autoregressive

texture model using information criteria.

Pattern Recognition Letters.

Alata, O. and C. Ramananjarasoa

(2005). Unsupervised textured image

segmentation using 2-D quarter plane

autoregressive support with four prediction

support. Pattern Recognition Letters,


Atto, A., Y. Berthoumieu, and P. Bolon

(2013). 2-dimensional wavelet packet spectrum

for texture analysis. IEEE Transactions on

Image Processing, 22(6):2495–500.

Atto, A., D. Pastor, and G. Mercier

(2010). Wavelet packets of fractional

brownian motion: Asymptotic analysis and

spectrum estimation. IEEE Transactions on

Information Theory, 56:4741 – 53.

Atto, A., Z. Tan, O. Alata, and M. Moreaud

(2014). Non-stationary texture synthesis from

random field modeling. In IEEE Int. Conf.

Image Processing, ICIP, Pp. 4266–70.

Celce, B., S. Bres, F. Moreau, P. Gueroult, and

L. Sorbier

(2008). Semi-automatic detection of

sulfur slabs. STERMAT 2008 : VIII

International Conference on Stereology

and Image Analysis in Materials Sciences,

–6 septembre 2008 Zakopane, Polska.

Inżynieria Materiałowa 29 (4) : 421–6.

Da Costa, J.-P., P. Weisbecker, B. Farbos,

J. Leyssale, G. Vignoles, and C. Germain

(2015). Investigating carbon materials

nanostructure using image orientation

statistics. Carbon, 84:160–73.

Fieguth, P. W. and A. S. Willsky

(1996). Fractal estimation using models on

multiscale trees. IEEE Trans. Signal Proc.,


Geantet, C. and L. Sorbier

(2012). Chapter 2.6 - Characterisation of

catalysts. STDI Frame Maker.

Geweke, J. and S. Porter-Hudak

(1983). The estimation and application of long

memory time series models. Journal of Time

Series Anal., 4:221–37.

Goncalves, W. and O. Bruno

(2013). Combining fractal and deterministic

walkers for texture analysis and classification.

Pattern Recognition, 46:2953–68.

Haralick, R. M.

(1979). Statistical and structural approaches to

texture. Proceedings of the IEEE, 67(5):786

– 804.

Huang, Q., J. R. Lorch, and R. C. Dubes

(1994). Can the fractal dimension of images be

measured? Pattern Recognition, 27(3):339–

Huang, Z. and C. Li

(2005). Anisotropic fractional brownian

random fields as white noise functionals. Acta

Mathematicae Applicatae Sinica, English

Series, 21(4):655–60.

Jackson, L. B. and H. C. Chien

(1979). Frequency and bearing estimation by

two-dimensional linear prediction. In IEEE

Int. Conf. Acoustic Speech and Sig. Proc.,

ICASSP, Pp. 665 – 8.

Kroese, D. P. and Z. I. Botev

(2013). Spatial process generation. Statistics


Mandelbrot, B. B. and J. W. V. Ness

(1968. Fractional Brownian motions, fractional

noises and application. SIAM Review,


Mao, J. and A. Jain

(1992). Texture classification and

segmentation using multi-resolution

simultaneous autoregressive (MR-SAR)

models. Pattern Recognition, 25(2):173–88.

Moreaud, M., D. Jeulin, V. Morard, and R. Revel.

(2012). TEM image analysis and modelling:

application to boehmites nanoparticles.

Journal of Microscopy, 245(2):186–99.

Moreaud, M., D. Jeulin, A. Thorel, and J. Y.


(2008). A quantitative morphological analysis

of nanostructured ceria–silica composite

catalysts. Journal of Microscopy, 232:293–

Nason, G. and B. Silverman

(1995). The stationary wavelet transform and

some statistical applications. Lecture Notes in

Statistics, 103:281–99.

Nikulshin, P., D. Ishutenko, A. Mozhaev,

K. Maslakov, and A. Pimerzin

(2014). Effects of composition and morphology

of active phase of CoMo/Al2O3 catalysts

prepared using Co2Mo10–heteropolyacid and

chelating agents on their catalytic properties

in HDS and HYD reactions. Journal of

Catalysis, 312:152–69.

Parzen, E.

(1962). On estimation of a probability density

function and mode. Ann. Math. Statist.,


Peacock, J.

(1983). Two-dimensional goodness-of-fit

testing in astronomy. Monthly Notices of the

Royal Astronomical Society, 202(3):615–27.

Pesquet-Popescu, B. and P. Larzabal

(1997). 2D self-similar processes with

stationary fractional increments. SpringerVerlag

in Fractals in Engineering, Pp. 138–

Pesquet-Popescu, B. and J. L. Véhel

(2002). Stochastic fractal models for

image processing. IEEE Signal Processing

Magazine, 19:48–62.

Pré, P., G. Huchet, D. Jeulin, J. Rouzaud,

M. Sennour, and A. Thorel

(2013). A new approach to characterize

the nanostructure of activated carbons from

mathematical morphology applied to high

resolution transmission electron microscopy

images. Carbon 52, Pp. 239–58.

Qazi, I.-U.-H., O. Alata, J.-C. Burie, A. Moussa,

and C. Fernandez-Maloigne

(2011). Choice of a pertinent color space for

color texture characterization using parametric

spectral analysis. Pattern Recognition

Letters, 44:16–31.

Ranganath, S. and A. K. Jain

(1985). Two-dimensional linear prediction

models - part I: spectral factorization and

realization. IEEE Trans. on Acoustic Speech

and Signal Processing, ASSP-33(1):280–99.

Richard, F. and H. Bierme

(2010). Statistical tests of anisotropy for

fractional Brownian textures. Application to

full-field digital mammography. Journal of

Mathematical Imaging and Vision, 36(3):227

– 40.

Robinson, P. M.

(1995). Log-periodogram regression of times

series with long range dependence. The

Annals of Statistics, 23(3):1048–72.

Rosenblatt, M.

(1956). Remarks on some nonparametric

estimates of a density function. Ann. Math.

Statist., 27:832–7.

Serra, J.

(1988). Image analysis and mathematical

morphology: Theoretical advances. Academic

Press, London.

Souza, P.

(1982). Texture recognition via autoregression.

Pattern Recognition, 15(6):471–5.

Tafti, P., D. Van De Ville, and M. Unser

(2009). Invariances, Laplacian-like wavelet

bases, and the whitening of fractal processes.

IEEE Trans. on Image Processing, 18:689 –

Tan, Z., A. Atto, O. Alata, and M. Moreaud

(2015). ARFBF model for non-stationary

random fields and application in HRTEM

images. In IEEE Int. Conf. on Image

Processing, ICIP.

Toth, P., A. Palotas, E. Eddings, R. Whitaker,

and J. Lighty

(2013). A novel framework for the quantitative

analysis of high resolution transmission

electron micrographs of soot II. Robust

multiscale nanostructure quantification.

Combustion and Flame, 160:920–32.

Toulhoat, H. and P. Raybaud

(2013). Catalysis by transition metal

sulphides - from molecular theory to industrial

application. IFP Publications.

Van De Ville, D., T. Blu, and M. Unser

(2005). Isotropic polyharmonic B-splines:

Scaling functions and wavelets. IEEE Trans.

on Image Processing, 14:1798 – 813.

Yehliu, K., R. V. Wal, and A. Boehman

(2011). Development of an HRTEM

image analysis method to quantify carbon

nanostructure. Combustion and Flame,


Zhang, B. S., Y. J. Yi, W. Zhang, C. H. Liang, and

D. S. Su

(2011). Electron microscopy investigation of

the microstructure of unsupported Ni-Mo-W

sulfide. Materials Characterization, 62:684–




How to Cite

Tan, Z., Moreaud, M., Alata, O., & Atto, A. M. (2018). ARFBF MORPHOLOGICAL ANALYSIS - APPLICATION TO THE DISCRIMINATION OF CATALYST ACTIVE PHASES. Image Analysis and Stereology, 37(1), 21–34.



Original Research Paper